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				<span style="position: absolute;left:15px;bottom:15px;width:90%;"><font class="view-text" style="color:#fcfcfc;font-size:25px">题解 P2774 【方格取数问题】</font><br><a href="/tags/2020/" class="tag"><span  style="background-color: rgb(52, 152, 219);">2020</span></a>&nbsp;<a href="/tags/最小割/" class="tag"><span  style="background-color: rgb(231, 76, 60);">最小割</span></a>&nbsp;<a href="/tags/网络流/" class="tag"><span  style="background-color: rgb(231, 76, 60);">网络流</span></a>&nbsp;<a href="/tags/题解/" class="tag"><span  style="background-color: rgb(82, 196, 26);">题解</span></a></span>
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                <h2 id="_1">题意</h2>
<p>在一个<script type="math/tex">m\times n</script>的方阵中取若干个数，任意两个数不能相邻，求和的最大值</p>
<!--more-->
<h2 id="_2">题解</h2>
<blockquote>
<p><strong>小技巧</strong>：在网络流建模的时候，如果关系比较类似，我们可以先考虑局部建模，再将其放到全局去考虑。</p>
</blockquote>
<p>在此题中，我们使用上面的方法，先拎出两个相邻的数<script type="math/tex">A</script>和<script type="math/tex">B</script>，用<script type="math/tex">X</script>和<script type="math/tex">Y</script>表示他们对应的点。</p>
<p>根据体面，我们了解到，对于<script type="math/tex">A</script>与<script type="math/tex">B</script>，其必定是<strong>二选一</strong>的。二选一<sub>~自然</sub>~能够想到的就是<strong>最小割</strong>了，把其选中若干个数使和最大，看作是选若干个<strong>矛盾的</strong>数使和最小，剩下的必然是不矛盾的 <del>最小割的套路</del>。然后我们就<sub>~很容易的想到了如下操作</sub>~</p>
<ol>
<li>将源点<script type="math/tex">S</script>与<script type="math/tex">X</script>连接一条删去费用为<script type="math/tex">A</script>的边</li>
<li>将<script type="math/tex">X</script>与<script type="math/tex">Y</script>连接一条删去费用为<script type="math/tex">+\infty</script>的边</li>
<li>将<script type="math/tex">Y</script>与汇点<script type="math/tex">T</script>连接一条删去费用为<script type="math/tex">B</script>的边</li>
</ol>
<p>所以我们现在的问题是把局部的两个点<strong>搬</strong>到整个方阵上去。<del>根据某个套路</del>，我们可以把所有的方格按照<script type="math/tex">(x+y) \bmod2</script>的值分类，那么对于在同一类中的数，是必定不会互相影响的。因此将<script type="math/tex">x+y</script>为奇数的当成上面的<script type="math/tex">X</script>点，<script type="math/tex">x+y</script>为偶数的当成<script type="math/tex">B</script>点，跑一遍最大流就 <script type="math/tex">\color{green}{\texttt{AC}}</script>了</p>
<h2 id="_3">代码</h2>
<div class="highlight"><pre><span></span><code><span class="linenos" data-linenos="  1 "></span> <span class="cp">#pragma GCC optimize(3,&quot;Ofast&quot;,&quot;inline&quot;)</span>
<span class="linenos" data-linenos="  2 "></span><span class="cp">#include</span><span class="cpf">&lt;bits/stdc++.h&gt;</span><span class="cp"></span>
<span class="linenos" data-linenos="  3 "></span><span class="k">namespace</span> <span class="n">in</span><span class="p">{</span>
<span class="linenos" data-linenos="  4 "></span>    <span class="kt">char</span> <span class="n">buf</span><span class="p">[</span><span class="mi">1</span><span class="o">&lt;&lt;</span><span class="mi">21</span><span class="p">],</span><span class="o">*</span><span class="n">p1</span><span class="o">=</span><span class="n">buf</span><span class="p">,</span><span class="o">*</span><span class="n">p2</span><span class="o">=</span><span class="n">buf</span><span class="p">;</span>
<span class="linenos" data-linenos="  5 "></span>    <span class="kr">inline</span> <span class="kt">int</span> <span class="n">getc</span><span class="p">(){</span>
<span class="linenos" data-linenos="  6 "></span>        <span class="k">return</span> <span class="n">p1</span><span class="o">==</span><span class="n">p2</span><span class="o">&amp;&amp;</span><span class="p">(</span><span class="n">p2</span><span class="o">=</span><span class="p">(</span><span class="n">p1</span><span class="o">=</span><span class="n">buf</span><span class="p">)</span><span class="o">+</span><span class="n">fread</span><span class="p">(</span><span class="n">buf</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="o">&lt;&lt;</span><span class="mi">21</span><span class="p">,</span><span class="n">stdin</span><span class="p">),</span><span class="n">p1</span><span class="o">==</span><span class="n">p2</span><span class="p">)</span><span class="o">?</span><span class="nl">EOF</span><span class="p">:</span><span class="o">*</span><span class="n">p1</span><span class="o">++</span><span class="p">;</span>
<span class="linenos" data-linenos="  7 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="  8 "></span>    <span class="k">template</span> <span class="o">&lt;</span><span class="k">typename</span> <span class="nc">T</span><span class="o">&gt;</span><span class="kr">inline</span> <span class="kt">void</span> <span class="n">read</span><span class="p">(</span><span class="n">T</span><span class="o">&amp;</span> <span class="n">t</span><span class="p">){</span>
<span class="linenos" data-linenos="  9 "></span>        <span class="n">t</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="kt">int</span> <span class="n">f</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="kt">char</span> <span class="n">ch</span><span class="o">=</span><span class="n">getc</span><span class="p">();</span>
<span class="linenos" data-linenos=" 10 "></span>        <span class="k">while</span> <span class="p">(</span><span class="o">!</span><span class="n">isdigit</span><span class="p">(</span><span class="n">ch</span><span class="p">)){</span>
<span class="linenos" data-linenos=" 11 "></span>            <span class="k">if</span><span class="p">(</span><span class="n">ch</span><span class="o">==</span><span class="sc">&#39;-&#39;</span><span class="p">)</span><span class="n">f</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 12 "></span>            <span class="n">ch</span><span class="o">=</span><span class="n">getc</span><span class="p">();</span>
<span class="linenos" data-linenos=" 13 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos=" 14 "></span>        <span class="k">while</span><span class="p">(</span><span class="n">isdigit</span><span class="p">(</span><span class="n">ch</span><span class="p">)){</span>
<span class="linenos" data-linenos=" 15 "></span>            <span class="n">t</span><span class="o">=</span><span class="n">t</span><span class="o">*</span><span class="mi">10</span><span class="o">+</span><span class="n">ch</span><span class="mi">-48</span><span class="p">;</span>
<span class="linenos" data-linenos=" 16 "></span>            <span class="n">ch</span> <span class="o">=</span> <span class="n">getc</span><span class="p">();</span>
<span class="linenos" data-linenos=" 17 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos=" 18 "></span>        <span class="k">if</span><span class="p">(</span><span class="n">f</span><span class="p">)</span><span class="n">t</span><span class="o">=-</span><span class="n">t</span><span class="p">;</span>
<span class="linenos" data-linenos=" 19 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos=" 20 "></span>    <span class="k">template</span> <span class="o">&lt;</span><span class="k">typename</span> <span class="nc">T</span><span class="p">,</span><span class="k">typename</span><span class="p">...</span> <span class="n">Args</span><span class="o">&gt;</span> <span class="kr">inline</span> <span class="kt">void</span> <span class="n">read</span><span class="p">(</span><span class="n">T</span><span class="o">&amp;</span> <span class="n">t</span><span class="p">,</span> <span class="n">Args</span><span class="o">&amp;</span><span class="p">...</span> <span class="n">args</span><span class="p">){</span>
<span class="linenos" data-linenos=" 21 "></span>        <span class="n">read</span><span class="p">(</span><span class="n">t</span><span class="p">);</span><span class="n">read</span><span class="p">(</span><span class="n">args</span><span class="p">...);</span>
<span class="linenos" data-linenos=" 22 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos=" 23 "></span><span class="p">}</span>
<span class="linenos" data-linenos=" 24 "></span><span class="k">namespace</span> <span class="n">out</span><span class="p">{</span>
<span class="linenos" data-linenos=" 25 "></span>    <span class="kt">char</span> <span class="n">buffer</span><span class="p">[</span><span class="mi">1</span><span class="o">&lt;&lt;</span><span class="mi">21</span><span class="p">];</span>
<span class="linenos" data-linenos=" 26 "></span>    <span class="kt">int</span> <span class="n">p1</span><span class="o">=</span><span class="mi">-1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 27 "></span>    <span class="k">const</span> <span class="kt">int</span> <span class="n">p2</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="o">&lt;&lt;</span><span class="mi">21</span><span class="p">)</span><span class="mi">-1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 28 "></span>    <span class="kr">inline</span> <span class="kt">void</span> <span class="n">flush</span><span class="p">()</span> <span class="p">{</span>
<span class="linenos" data-linenos=" 29 "></span>        <span class="n">fwrite</span><span class="p">(</span><span class="n">buffer</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="n">p1</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">stdout</span><span class="p">),</span>
<span class="linenos" data-linenos=" 30 "></span>        <span class="n">p1</span><span class="o">=</span><span class="mi">-1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 31 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos=" 32 "></span>    <span class="kr">inline</span> <span class="kt">void</span> <span class="n">putc</span><span class="p">(</span><span class="k">const</span> <span class="kt">char</span> <span class="o">&amp;</span><span class="n">x</span><span class="p">)</span> <span class="p">{</span>
<span class="linenos" data-linenos=" 33 "></span>        <span class="k">if</span><span class="p">(</span><span class="n">p1</span><span class="o">==</span><span class="n">p2</span><span class="p">)</span><span class="n">flush</span><span class="p">();</span>
<span class="linenos" data-linenos=" 34 "></span>        <span class="n">buffer</span><span class="p">[</span><span class="o">++</span><span class="n">p1</span><span class="p">]</span><span class="o">=</span><span class="n">x</span><span class="p">;</span>
<span class="linenos" data-linenos=" 35 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos=" 36 "></span>    <span class="k">template</span> <span class="o">&lt;</span><span class="k">typename</span> <span class="nc">T</span><span class="o">&gt;</span><span class="kt">void</span> <span class="n">write</span><span class="p">(</span><span class="n">T</span> <span class="n">x</span><span class="p">)</span> <span class="p">{</span>
<span class="linenos" data-linenos=" 37 "></span>        <span class="k">static</span> <span class="kt">char</span> <span class="n">buf</span><span class="p">[</span><span class="mi">15</span><span class="p">];</span>
<span class="linenos" data-linenos=" 38 "></span>        <span class="k">static</span> <span class="kt">int</span> <span class="n">len</span><span class="o">=</span><span class="mi">-1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 39 "></span>        <span class="k">if</span><span class="p">(</span><span class="n">x</span><span class="o">&gt;=</span><span class="mi">0</span><span class="p">){</span>
<span class="linenos" data-linenos=" 40 "></span>            <span class="k">do</span><span class="p">{</span>
<span class="linenos" data-linenos=" 41 "></span>                <span class="n">buf</span><span class="p">[</span><span class="o">++</span><span class="n">len</span><span class="p">]</span><span class="o">=</span><span class="n">x</span><span class="o">%</span><span class="mi">10</span><span class="o">+</span><span class="mi">48</span><span class="p">,</span><span class="n">x</span><span class="o">/=</span><span class="mi">10</span><span class="p">;</span>
<span class="linenos" data-linenos=" 42 "></span>            <span class="p">}</span><span class="k">while</span> <span class="p">(</span><span class="n">x</span><span class="p">);</span>
<span class="linenos" data-linenos=" 43 "></span>        <span class="p">}</span><span class="k">else</span><span class="p">{</span>
<span class="linenos" data-linenos=" 44 "></span>            <span class="n">putc</span><span class="p">(</span><span class="sc">&#39;-&#39;</span><span class="p">);</span>
<span class="linenos" data-linenos=" 45 "></span>            <span class="k">do</span> <span class="p">{</span>
<span class="linenos" data-linenos=" 46 "></span>                <span class="n">buf</span><span class="p">[</span><span class="o">++</span><span class="n">len</span><span class="p">]</span><span class="o">=-</span><span class="p">(</span><span class="n">x</span><span class="o">%</span><span class="mi">10</span><span class="p">)</span><span class="o">+</span><span class="mi">48</span><span class="p">,</span><span class="n">x</span><span class="o">/=</span><span class="mi">10</span><span class="p">;</span>
<span class="linenos" data-linenos=" 47 "></span>            <span class="p">}</span><span class="k">while</span><span class="p">(</span><span class="n">x</span><span class="p">);</span>
<span class="linenos" data-linenos=" 48 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos=" 49 "></span>        <span class="k">while</span> <span class="p">(</span><span class="n">len</span><span class="o">&gt;=</span><span class="mi">0</span><span class="p">)</span>
<span class="linenos" data-linenos=" 50 "></span>            <span class="n">putc</span><span class="p">(</span><span class="n">buf</span><span class="p">[</span><span class="n">len</span><span class="p">]),</span><span class="o">--</span><span class="n">len</span><span class="p">;</span>
<span class="linenos" data-linenos=" 51 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos=" 52 "></span><span class="p">}</span>
<span class="linenos" data-linenos=" 53 "></span><span class="k">const</span> <span class="kt">int</span> <span class="n">maxn</span><span class="o">=</span><span class="mi">10000</span><span class="o">+</span><span class="mi">10</span><span class="p">,</span><span class="n">maxe</span><span class="o">=</span><span class="mi">1000000</span><span class="p">;</span>
<span class="linenos" data-linenos=" 54 "></span><span class="k">struct</span> <span class="nc">Graph</span><span class="p">{</span>
<span class="linenos" data-linenos=" 55 "></span>    <span class="k">struct</span> <span class="nc">node</span><span class="p">{</span>
<span class="linenos" data-linenos=" 56 "></span>        <span class="kt">int</span> <span class="n">v</span><span class="p">,</span><span class="n">w</span><span class="p">,</span><span class="n">nxt</span><span class="p">;</span>
<span class="linenos" data-linenos=" 57 "></span>        <span class="n">node</span><span class="p">(</span><span class="kt">int</span> <span class="n">_v</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="kt">int</span> <span class="n">_w</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="kt">int</span> <span class="n">_nxt</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span><span class="o">:</span><span class="n">v</span><span class="p">(</span><span class="n">_v</span><span class="p">),</span><span class="n">w</span><span class="p">(</span><span class="n">_w</span><span class="p">),</span><span class="n">nxt</span><span class="p">(</span><span class="n">_nxt</span><span class="p">){}</span>
<span class="linenos" data-linenos=" 58 "></span>    <span class="p">}</span><span class="n">e</span><span class="p">[</span><span class="n">maxe</span><span class="p">];</span>
<span class="linenos" data-linenos=" 59 "></span>    <span class="kt">int</span> <span class="n">head</span><span class="p">[</span><span class="n">maxn</span><span class="p">],</span><span class="n">cur</span><span class="p">[</span><span class="n">maxn</span><span class="p">],</span><span class="n">cnt</span><span class="p">;</span>
<span class="linenos" data-linenos=" 60 "></span>    <span class="kt">int</span> <span class="n">s</span><span class="p">,</span><span class="n">t</span><span class="p">,</span><span class="n">dis</span><span class="p">[</span><span class="n">maxn</span><span class="p">];</span>
<span class="linenos" data-linenos=" 61 "></span>    <span class="kr">inline</span> <span class="kt">void</span> <span class="n">init</span><span class="p">(</span><span class="kt">int</span> <span class="n">_s</span><span class="p">,</span><span class="kt">int</span> <span class="n">_t</span><span class="p">){</span><span class="n">s</span><span class="o">=</span><span class="n">_s</span><span class="p">,</span><span class="n">t</span><span class="o">=</span><span class="n">_t</span><span class="p">;</span><span class="n">cnt</span><span class="o">=</span><span class="mi">1</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 62 "></span>    <span class="kt">void</span> <span class="n">add</span><span class="p">(</span><span class="kt">int</span> <span class="n">u</span><span class="p">,</span><span class="kt">int</span> <span class="n">v</span><span class="p">,</span><span class="kt">int</span> <span class="n">w</span><span class="p">){</span>
<span class="linenos" data-linenos=" 63 "></span>        <span class="n">e</span><span class="p">[</span><span class="o">++</span><span class="n">cnt</span><span class="p">]</span><span class="o">=</span><span class="n">node</span><span class="p">(</span><span class="n">v</span><span class="p">,</span><span class="n">w</span><span class="p">,</span><span class="n">head</span><span class="p">[</span><span class="n">u</span><span class="p">]);</span><span class="n">head</span><span class="p">[</span><span class="n">u</span><span class="p">]</span><span class="o">=</span><span class="n">cnt</span><span class="p">;</span>
<span class="linenos" data-linenos=" 64 "></span>        <span class="n">e</span><span class="p">[</span><span class="o">++</span><span class="n">cnt</span><span class="p">]</span><span class="o">=</span><span class="n">node</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="n">head</span><span class="p">[</span><span class="n">v</span><span class="p">]);</span><span class="n">head</span><span class="p">[</span><span class="n">v</span><span class="p">]</span><span class="o">=</span><span class="n">cnt</span><span class="p">;</span>
<span class="linenos" data-linenos=" 65 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos=" 66 "></span>    <span class="cp">#define v e[i].v</span>
<span class="linenos" data-linenos=" 67 "></span>    <span class="kr">inline</span> <span class="kt">bool</span> <span class="n">bfs</span><span class="p">(){</span>
<span class="linenos" data-linenos=" 68 "></span>        <span class="n">memset</span><span class="p">(</span><span class="n">dis</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="k">sizeof</span> <span class="n">dis</span><span class="p">);</span>
<span class="linenos" data-linenos=" 69 "></span>        <span class="n">memcpy</span><span class="p">(</span><span class="n">cur</span><span class="p">,</span><span class="n">head</span><span class="p">,</span><span class="k">sizeof</span> <span class="n">cur</span><span class="p">);</span>
<span class="linenos" data-linenos=" 70 "></span>        <span class="n">std</span><span class="o">::</span><span class="n">queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="n">q</span><span class="p">;</span>
<span class="linenos" data-linenos=" 71 "></span>        <span class="n">q</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">s</span><span class="p">);</span><span class="n">dis</span><span class="p">[</span><span class="n">s</span><span class="p">]</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 72 "></span>        <span class="k">while</span><span class="p">(</span><span class="o">!</span><span class="n">q</span><span class="p">.</span><span class="n">empty</span><span class="p">()){</span>
<span class="linenos" data-linenos=" 73 "></span>            <span class="kt">int</span> <span class="n">u</span><span class="o">=</span><span class="n">q</span><span class="p">.</span><span class="n">front</span><span class="p">();</span><span class="n">q</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
<span class="linenos" data-linenos=" 74 "></span>            <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="n">head</span><span class="p">[</span><span class="n">u</span><span class="p">];</span><span class="n">i</span><span class="p">;</span><span class="n">i</span><span class="o">=</span><span class="n">e</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">nxt</span><span class="p">)</span><span class="k">if</span><span class="p">(</span><span class="n">e</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">w</span><span class="o">&amp;&amp;!</span><span class="n">dis</span><span class="p">[</span><span class="n">v</span><span class="p">]){</span>
<span class="linenos" data-linenos=" 75 "></span>                <span class="n">dis</span><span class="p">[</span><span class="n">v</span><span class="p">]</span><span class="o">=</span><span class="n">dis</span><span class="p">[</span><span class="n">u</span><span class="p">]</span><span class="o">+</span><span class="mi">1</span><span class="p">;</span><span class="n">q</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">v</span><span class="p">);</span>
<span class="linenos" data-linenos=" 76 "></span>                <span class="k">if</span><span class="p">(</span><span class="n">v</span><span class="o">==</span><span class="n">t</span><span class="p">)</span><span class="k">return</span> <span class="nb">true</span><span class="p">;</span>
<span class="linenos" data-linenos=" 77 "></span>            <span class="p">}</span>
<span class="linenos" data-linenos=" 78 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos=" 79 "></span>        <span class="k">return</span> <span class="nb">false</span><span class="p">;</span>
<span class="linenos" data-linenos=" 80 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos=" 81 "></span>    <span class="kt">int</span> <span class="n">dfs</span><span class="p">(</span><span class="kt">int</span> <span class="n">u</span><span class="p">,</span><span class="kt">int</span> <span class="n">flow</span><span class="p">){</span>
<span class="linenos" data-linenos=" 82 "></span>        <span class="k">if</span><span class="p">(</span><span class="n">u</span><span class="o">==</span><span class="n">t</span><span class="p">)</span><span class="k">return</span> <span class="n">flow</span><span class="p">;</span>
<span class="linenos" data-linenos=" 83 "></span>        <span class="kt">int</span> <span class="n">rest</span><span class="o">=</span><span class="n">flow</span><span class="p">;</span>
<span class="linenos" data-linenos=" 84 "></span>        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="o">&amp;</span><span class="n">i</span><span class="o">=</span><span class="n">cur</span><span class="p">[</span><span class="n">u</span><span class="p">];</span><span class="n">i</span><span class="p">;</span><span class="n">i</span><span class="o">=</span><span class="n">e</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">nxt</span><span class="p">){</span>
<span class="linenos" data-linenos=" 85 "></span>            <span class="k">if</span><span class="p">(</span><span class="n">dis</span><span class="p">[</span><span class="n">v</span><span class="p">]</span><span class="o">==</span><span class="n">dis</span><span class="p">[</span><span class="n">u</span><span class="p">]</span><span class="o">+</span><span class="mi">1</span><span class="o">&amp;&amp;</span><span class="n">e</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">w</span><span class="p">){</span>
<span class="linenos" data-linenos=" 86 "></span>                <span class="kt">int</span> <span class="n">tmp</span><span class="o">=</span><span class="n">dfs</span><span class="p">(</span><span class="n">v</span><span class="p">,</span><span class="n">std</span><span class="o">::</span><span class="n">min</span><span class="p">(</span><span class="n">rest</span><span class="p">,</span><span class="n">e</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">w</span><span class="p">));</span>
<span class="linenos" data-linenos=" 87 "></span>                <span class="n">e</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">w</span><span class="o">-=</span><span class="n">tmp</span><span class="p">,</span><span class="n">e</span><span class="p">[</span><span class="n">i</span><span class="o">^</span><span class="mi">1</span><span class="p">].</span><span class="n">w</span><span class="o">+=</span><span class="n">tmp</span><span class="p">,</span><span class="n">rest</span><span class="o">-=</span><span class="n">tmp</span><span class="p">;</span>
<span class="linenos" data-linenos=" 88 "></span>            <span class="p">}</span>
<span class="linenos" data-linenos=" 89 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos=" 90 "></span>        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">rest</span><span class="p">)</span><span class="n">dis</span><span class="p">[</span><span class="n">u</span><span class="p">]</span><span class="o">=</span><span class="mi">-1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 91 "></span>        <span class="k">return</span> <span class="n">flow</span><span class="o">-</span><span class="n">rest</span><span class="p">;</span>
<span class="linenos" data-linenos=" 92 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos=" 93 "></span>    <span class="cp">#undef v</span>
<span class="linenos" data-linenos=" 94 "></span>    <span class="kt">int</span> <span class="n">dinic</span><span class="p">(){</span>
<span class="linenos" data-linenos=" 95 "></span>        <span class="kt">int</span> <span class="n">ans</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
<span class="linenos" data-linenos=" 96 "></span>        <span class="k">while</span><span class="p">(</span><span class="n">bfs</span><span class="p">())</span>
<span class="linenos" data-linenos=" 97 "></span>            <span class="k">while</span><span class="p">(</span><span class="kt">int</span> <span class="n">sth</span><span class="o">=</span><span class="n">dfs</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="mf">2e9</span><span class="p">))</span>
<span class="linenos" data-linenos=" 98 "></span>                <span class="n">ans</span><span class="o">+=</span><span class="n">sth</span><span class="p">;</span>
<span class="linenos" data-linenos=" 99 "></span>        <span class="k">return</span> <span class="n">ans</span><span class="p">;</span>
<span class="linenos" data-linenos="100 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="101 "></span><span class="p">}</span><span class="n">G</span><span class="p">;</span>
<span class="linenos" data-linenos="102 "></span><span class="kt">int</span> <span class="n">m</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">x</span><span class="p">,</span><span class="n">sum</span><span class="p">;</span><span class="c1">//m为行数 n为列数</span>
<span class="linenos" data-linenos="103 "></span><span class="cp">#define P(i,j) ((i)-1)*n+(j) </span>
<span class="linenos" data-linenos="104 "></span><span class="kr">inline</span> <span class="kt">bool</span> <span class="n">check</span><span class="p">(</span><span class="kt">int</span> <span class="n">x</span><span class="p">,</span><span class="kt">int</span> <span class="n">y</span><span class="p">){</span>
<span class="linenos" data-linenos="105 "></span>    <span class="k">return</span> <span class="n">x</span><span class="o">&lt;=</span><span class="n">m</span><span class="o">&amp;&amp;</span><span class="n">x</span><span class="o">&gt;=</span><span class="mi">1</span><span class="o">&amp;&amp;</span><span class="n">y</span><span class="o">&lt;=</span><span class="n">n</span><span class="o">&amp;&amp;</span><span class="n">y</span><span class="o">&gt;=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos="106 "></span><span class="p">}</span>
<span class="linenos" data-linenos="107 "></span><span class="kt">signed</span> <span class="n">main</span><span class="p">(){</span>
<span class="linenos" data-linenos="108 "></span>    <span class="n">in</span><span class="o">::</span><span class="n">read</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="n">n</span><span class="p">);</span>
<span class="linenos" data-linenos="109 "></span>    <span class="n">G</span><span class="p">.</span><span class="n">init</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="n">n</span><span class="o">*</span><span class="n">m</span><span class="o">+</span><span class="mi">1</span><span class="p">);</span>
<span class="linenos" data-linenos="110 "></span>    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;=</span><span class="n">m</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="111 "></span>        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">j</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">j</span><span class="o">&lt;=</span><span class="n">n</span><span class="p">;</span><span class="n">j</span><span class="o">++</span><span class="p">){</span>
<span class="linenos" data-linenos="112 "></span>            <span class="n">in</span><span class="o">::</span><span class="n">read</span><span class="p">(</span><span class="n">x</span><span class="p">);</span><span class="n">sum</span><span class="o">+=</span><span class="n">x</span><span class="p">;</span>
<span class="linenos" data-linenos="113 "></span>            <span class="k">if</span><span class="p">((</span><span class="n">i</span><span class="o">+</span><span class="n">j</span><span class="p">)</span><span class="o">&amp;</span><span class="mi">1</span><span class="p">){</span>
<span class="linenos" data-linenos="114 "></span>                <span class="n">G</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">G</span><span class="p">.</span><span class="n">s</span><span class="p">,</span><span class="n">P</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">),</span><span class="n">x</span><span class="p">);</span>
<span class="linenos" data-linenos="115 "></span>                <span class="k">if</span><span class="p">(</span><span class="n">check</span><span class="p">(</span><span class="n">i</span><span class="mi">-1</span><span class="p">,</span><span class="n">j</span><span class="p">))</span><span class="n">G</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">P</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">),</span><span class="n">P</span><span class="p">(</span><span class="n">i</span><span class="mi">-1</span><span class="p">,</span><span class="n">j</span><span class="p">),</span><span class="mf">1e9</span><span class="p">);</span>
<span class="linenos" data-linenos="116 "></span>                <span class="k">if</span><span class="p">(</span><span class="n">check</span><span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">j</span><span class="p">))</span><span class="n">G</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">P</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">),</span><span class="n">P</span><span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">j</span><span class="p">),</span><span class="mf">1e9</span><span class="p">);</span>
<span class="linenos" data-linenos="117 "></span>                <span class="k">if</span><span class="p">(</span><span class="n">check</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="mi">-1</span><span class="p">))</span><span class="n">G</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">P</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">),</span><span class="n">P</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="mi">-1</span><span class="p">),</span><span class="mf">1e9</span><span class="p">);</span>
<span class="linenos" data-linenos="118 "></span>                <span class="k">if</span><span class="p">(</span><span class="n">check</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span><span class="n">G</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">P</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">),</span><span class="n">P</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">),</span><span class="mf">1e9</span><span class="p">);</span>
<span class="linenos" data-linenos="119 "></span>
<span class="linenos" data-linenos="120 "></span>            <span class="p">}</span>
<span class="linenos" data-linenos="121 "></span>            <span class="k">else</span><span class="p">{</span>
<span class="linenos" data-linenos="122 "></span>                <span class="n">G</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">P</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">),</span><span class="n">G</span><span class="p">.</span><span class="n">t</span><span class="p">,</span><span class="n">x</span><span class="p">);</span>
<span class="linenos" data-linenos="123 "></span>            <span class="p">}</span>
<span class="linenos" data-linenos="124 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos="125 "></span>    <span class="n">out</span><span class="o">::</span><span class="n">write</span><span class="p">(</span><span class="n">sum</span><span class="o">-</span><span class="n">G</span><span class="p">.</span><span class="n">dinic</span><span class="p">());</span>
<span class="linenos" data-linenos="126 "></span>    <span class="n">out</span><span class="o">::</span><span class="n">flush</span><span class="p">();</span>
<span class="linenos" data-linenos="127 "></span>    <span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
<span class="linenos" data-linenos="128 "></span><span class="p">}</span>
</code></pre></div>
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    <span><font style="font-weight: bold">题解 P2774 【方格取数问题】</font></span>
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